A 3D-Schrödinger operator under magnetic steps with semiclassical applications

Assaad, Wafaa and Giacomelli, Emanuela L. (2022): A 3D-Schrödinger operator under magnetic steps with semiclassical applications. In: Discrete and Continuous Dynamical Systems, Vol. 43, No. 2: pp. 619-660

Abstract

We define a Schrodinger operator on the half-space with a dis-continuous magnetic field having a piecewise-constant strength and a uniform direction. Motivated by applications in the theory of superconductivity, we study the infimum of the spectrum of the operator. We give sufficient con-ditions on the strength and the direction of the magnetic field such that the aforementioned infimum is an eigenvalue of a reduced model operator on the half-plane. We use the Schrodinger operator on the half-space to study a new semiclassical problem in bounded domains of the space, considering a magnetic Neumann Laplacian with a piecewise-constant magnetic field. We then make precise the localization of the semiclassical ground state near specific points at the discontinuity jump of the magnetic field.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Computer Science
• Subjects: 000 Computer science, information and general works > 004 Data processing computer science
• ISSN: 1078-0947
• Language: English